# ---
# title: 1434. Number of Ways to Wear Different Hats to Each Other
# id: problem1434
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Dynamic Programming, Bit Manipulation
# link: <https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other/description/>
# hidden: true
# ---
# 
# There are `n` people and 40 types of hats labeled from 1 to 40.
# 
# Given a list of list of integers `hats`, where `hats[i]` is a list of all hats
# preferred by the `i-th` person.
# 
# Return the number of ways that the n people wear different hats to each other.
# 
# Since the answer may be too large, return it modulo `10^9 + 7`.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: hats = [[3,4],[4,5],[5]]
#     Output: 1
#     Explanation: There is only one way to choose hats given the conditions. 
#     First person choose hat 3, Second person choose hat 4 and last one hat 5.
# 
# **Example 2:**
# 
#     
#     
#     Input: hats = [[3,5,1],[3,5]]
#     Output: 4
#     Explanation: There are 4 ways to choose hats
#     (3,5), (5,3), (1,3) and (1,5)
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: hats = [[1,2,3,4],[1,2,3,4],[1,2,3,4],[1,2,3,4]]
#     Output: 24
#     Explanation: Each person can choose hats labeled from 1 to 4.
#     Number of Permutations of (1,2,3,4) = 24.
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: hats = [[1,2,3],[2,3,5,6],[1,3,7,9],[1,8,9],[2,5,7]]
#     Output: 111
#     
# 
# 
# 
# **Constraints:**
# 
#   * `n == hats.length`
#   * `1 <= n <= 10`
#   * `1 <= hats[i].length <= 40`
#   * `1 <= hats[i][j] <= 40`
#   * `hats[i]` contains a list of **unique** integers.
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
